set f = X --> (0. Y);
reconsider f = X --> (0. Y) as Function of X,Y ;
dom f = X by FUNCT_2:def 1;
then reconsider g = f as PartFunc of REAL,Y by RELSET_1:5;
dom g = X by FUNCT_2:def 1;
hence not ContinuousFunctions (X,Y) is empty by Def2; :: thesis: verum